A fundamental assumption in IRT model-based adaptive testing is that matching difficulty levels of test items with an examinee's ability makes a test more efficient. According to Lord, "An examinee is measured most effectively when the test items are neither too difficult nor too easy for him." This assumption is examined and challenged under a class one-parameter IRT models including those of the Rasch and the normal ogive. It is found that for a specific model, the validity of the fundamental assumption is closely related to the so-called van Zwet tail ordering for symmetric distributions. In this connection, the cosine distribution may serve as the borderline between those satisfying the assumption and those violates the assumption. Graphic and numerical illustrations are given to illustrate the theoretic results.
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